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INTEGRALLAR TABLICASÍ
[eng: table of integrals, рус: таблица интегралов]
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21.02.2024 02:16
INTEGRALLAR TABLICASÍ [en: table of integrals, ru: таблица интегралов]
– integrallar tablicasın tuwındılar tablicası járdeminde dúziw múmkin: $$ \begin{array}{|c|c|c|} \hline No & funkciya f(x) & dáslepki funkciya : F(x)+C \\ \hline 1 & x^p, p\neq-1 & \displaystyle\frac{x^{p+1}}{p+1}+C \\ \hline 2 & \dfrac{1}{x} & \ln|x|+C \\\hline 3 & e^x & e^x+C \\\hline 4 & \sin x & -\cos x+C\\\hline 5 &\cos x &\sin x+C\\\hline 6&(kx+b)^p, p\neq-1, k\neq0&\displaystyle\frac{(kx+b)^{p+1}}{k(p+1)}+C\\\hline7&\displaystyle\frac{1}{kx+b}, k\neq0&\displaystyle\frac{1}{k}\ln|kx+b|+C\\\hline8&e^{kx+b}, k\neq 0&\displaystyle\frac{1}{k}e^{kx+b}+C\\\hline9&\sin(kx+b), k\neq0&-\displaystyle\frac{1}{k}\cos(kx+b)+C\\\hline10&\cos(kx+b), k\neq0&\displaystyle\frac{1}{k}\sin(kx+b)+C\\\hline11&\displaystyle\frac{1}{\cos^2 x}&\text{tg} x+C\\\hline12&\displaystyle\frac{1}{\sin^2 x}&-\text{ctg}x+C\\\hline13&a^x&\displaystyle\frac{a^x}{\ln a}+C\\\hline14&\displaystyle\frac{1}{1+x^2}&\text{arctg}x+C\\\hline15&f(kx+b)&\displaystyle\frac{1}{k}F(kx+b)+C\\\hline16&f(g(x))g'(x)&F(g(x))+C\\\hline\end{array} $$